This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. Both ESR and NMR relaxation have proved useful in the study of protein dynamics. We have pioneered the slowly-relaxing local structure (SRLS) approach to their interpretation. It has been very successful, especially for the slow-motional ESR spectra, in this regard. In its present, relatively convenient implementations, the SRLS approaches are still computationally demanding;they are based on the simplification of (overdamped) diffusive motions, and are a mesoscopic (as distinct from an atomic) approach. This project was undertaken to provide improvements on the SRLS approach. For example, a protein side-chain which reorients in a potential well, will exhibit inertial effects in the form of torsional oscillations. Also the backbone dynamics of a protein necessarily involves collective dynamics, which could, in a relatively simple manner, be modeled by the coupling of several inertial linear rotators in the presence of global diffusion. Another objective is to obtain limiting analytical models that reduce the computational challenges in application to ESR and NMR spin relaxation, and to determine their range of validity.